How do you know that Ged's main fight will be against himself? Because his main rival in school is named Jasper. Has anyone named Jasper ever been really villainous? We don't think so.
Jasper comes from a wealthy family – he's the son of a lord on Havnor Isle (my, my). And whereas Ged seems at ease with poor families (9.3), Jasper is quite comfy with wealthy lords and ladies (3.85). Since he hails from a very wealthy family, he maybe looks down on Ged – or, at least, Ged thinks Jasper looks down on him. Check out their first meeting again: Jasper doesn't seem so nice, but Ged seems pretty rude, too, so it's not surprising that Jasper is rude right back. It's true that, later, Jasper becomes more condescending towards Ged, but it seems like there's the possibility that that first meeting could've gone differently if Ged weren't so proud. (Or not. Maybe Jasper's natural setting is "jerk." It's just so hard to tell.)
But then we get another hint: "Ged did not stop to think why Jasper might hate him. He only knew why he hated Jasper" (3.64). That's kind of a funny thing to say because it almost implies that Jasper might have a reason for hating Ged. In a usual school story – like Ender's Game or the first Harry Potter book – we have a rival (or rivals) and we don't really care what that "villainous" person thinks. But here, we get a little clue that Jasper might have his very own thoughts and feelings.
Now, that's all stuff that would make Jasper interesting as a character in another school story, but let's not forget that his main role in this book is as Ged's rival and to provide Ged with a reason to do dumb things now and then. That is, Ged thinks he's pretty great as a magician, but he only takes it to another level and does dumb stuff in order to prove himself to Jasper, the one kid at school who won't admit that Ged is great (3.64).